Some Are Not

[johnawysham]

The problem I have concerns the definition for "some are not". On page 403, at the top, 'some are not' is defined as "at least one is not, possibly all are not". Yet on page 405, in the middle of the page, 'some are not' is defined as 0 to 99 on a 0 to 100 unit scale. Since 0 to 99 does not include all 101 units on the 0 to 100 unit scale (100 not being included and 100 being the 101st unit), this definition of 'some are not' does not match the requirement for 'some are not' spelled out on page 403. I cannot see any way around this contradiction for 'some are not'. Can any reader explain this apparent contradiction between the definition of 'some are not' on page 403 and the definition of 'some are not' on page 405?

John Wysham

[Dave Killoran]

Hey John,

Thanks for the question! I think this is a case where you need to stop for a second and re-examine what is being said there and then examine the scale itself. I think you got caught up in counting items and missed a point along the way that was crucial to your analysis. Let's take a closer look and I think you'll conclude afterwards that what is being said there is perfectly in harmony with the scale used.

First, the scale is 0 to 100. As you noted, that has 101 discrete numbers. The definition of "some are not" is indeed as stated, "at least one is not, possibly all are not." That means everything but 100 is possible. Thus, using our 0 to 100 scale, that means we take 100 out, leaving 0 to 99. Everything said so far is actually consistent, but I believe you thought that there were 101 outcomes and if you removed the number 100 that left you with 100 outcomes, but then that 0 to 99 only had 99 outcomes. That's the problem right there: 0 to 99 is actually 100 outcomes because you count the number 0. I think you looked at 99 and thought it didn't match, but it actually does. In short, everything but 100 is 100 outcomes, and 0 to 99 is 100 outcomes. It all matches perfectly

Side note here: one of the nice things about the fact that these books have been around for a while and that I also actively update them every year and speak with students daily about them is that there are very few mistakes in them (and none that I know, actually). While I certainly won't rule out that an error could be found, on the major points such as something like this or a question explanation, it's very unlikely to be in error.

So, please take a look at that again and see if it makes sense; I feel confident it will. Thanks!